void clipLineSegmentToNearPlane(
    vec3 p0,
    vec3 p1,
    out vec4 positionWC,
    out bool clipped,
    out bool culledByNearPlane,
    out vec4 clippedPositionEC)
{
    culledByNearPlane = false;
    clipped = false;

    vec3 p0ToP1 = p1 - p0;
    float magnitude = length(p0ToP1);
    vec3 direction = normalize(p0ToP1);

    // Distance that p0 is behind the near plane. Negative means p0 is
    // in front of the near plane.
    float endPoint0Distance =  czm_currentFrustum.x + p0.z;

    // Camera looks down -Z.
    // When moving a point along +Z: LESS VISIBLE
    //   * Points in front of the camera move closer to the camera.
    //   * Points behind the camrea move farther away from the camera.
    // When moving a point along -Z: MORE VISIBLE
    //   * Points in front of the camera move farther away from the camera.
    //   * Points behind the camera move closer to the camera.

    // Positive denominator: -Z, becoming more visible
    // Negative denominator: +Z, becoming less visible
    // Nearly zero: parallel to near plane
    float denominator = -direction.z;

    if (endPoint0Distance > 0.0 && abs(denominator) < czm_epsilon7)
    {
        // p0 is behind the near plane and the line to p1 is nearly parallel to
        // the near plane, so cull the segment completely.
        culledByNearPlane = true;
    }
    else if (endPoint0Distance > 0.0)
    {
        // p0 is behind the near plane, and the line to p1 is moving distinctly
        // toward or away from it.

        // t = (-plane distance - dot(plane normal, ray origin)) / dot(plane normal, ray direction)
        float t = endPoint0Distance / denominator;
        if (t < 0.0 || t > magnitude)
        {
            // Near plane intersection is not between the two points.
            // We already confirmed p0 is behind the naer plane, so now
            // we know the entire segment is behind it.
            culledByNearPlane = true;
        }
        else
        {
            // Segment crosses the near plane, update p0 to lie exactly on it.
            p0 = p0 + t * direction;

            // Numerical noise might put us a bit on the wrong side of the near plane.
            // Don't let that happen.
            p0.z = min(p0.z, -czm_currentFrustum.x);

            clipped = true;
        }
    }

    clippedPositionEC = vec4(p0, 1.0);
    positionWC = czm_eyeToWindowCoordinates(clippedPositionEC);
}

vec4 getPolylineWindowCoordinatesEC(vec4 positionEC, vec4 prevEC, vec4 nextEC, float expandDirection, float width, bool usePrevious, out float angle)
{
    // expandDirection +1 is to the _left_ when looking from positionEC toward nextEC.

#ifdef POLYLINE_DASH
    // Compute the window coordinates of the points.
    vec4 positionWindow = czm_eyeToWindowCoordinates(positionEC);
    vec4 previousWindow = czm_eyeToWindowCoordinates(prevEC);
    vec4 nextWindow = czm_eyeToWindowCoordinates(nextEC);

    // Determine the relative screen space direction of the line.
    vec2 lineDir;
    if (usePrevious) {
        lineDir = normalize(positionWindow.xy - previousWindow.xy);
    }
    else {
        lineDir = normalize(nextWindow.xy - positionWindow.xy);
    }
    angle = atan(lineDir.x, lineDir.y) - 1.570796327; // precomputed atan(1,0)

    // Quantize the angle so it doesn't change rapidly between segments.
    angle = floor(angle / czm_piOverFour + 0.5) * czm_piOverFour;
#endif

    vec4 clippedPrevWC, clippedPrevEC;
    bool prevSegmentClipped, prevSegmentCulled;
    clipLineSegmentToNearPlane(prevEC.xyz, positionEC.xyz, clippedPrevWC, prevSegmentClipped, prevSegmentCulled, clippedPrevEC);

    vec4 clippedNextWC, clippedNextEC;
    bool nextSegmentClipped, nextSegmentCulled;
    clipLineSegmentToNearPlane(nextEC.xyz, positionEC.xyz, clippedNextWC, nextSegmentClipped, nextSegmentCulled, clippedNextEC);

    bool segmentClipped, segmentCulled;
    vec4 clippedPositionWC, clippedPositionEC;
    clipLineSegmentToNearPlane(positionEC.xyz, usePrevious ? prevEC.xyz : nextEC.xyz, clippedPositionWC, segmentClipped, segmentCulled, clippedPositionEC);

    if (segmentCulled)
    {
        return vec4(0.0, 0.0, 0.0, 1.0);
    }

    vec2 directionToPrevWC = normalize(clippedPrevWC.xy - clippedPositionWC.xy);
    vec2 directionToNextWC = normalize(clippedNextWC.xy - clippedPositionWC.xy);

    // If a segment was culled, we can't use the corresponding direction
    // computed above. We should never see both of these be true without
    // `segmentCulled` above also being true.
    if (prevSegmentCulled)
    {
        directionToPrevWC = -directionToNextWC;
    }
    else if (nextSegmentCulled)
    {
        directionToNextWC = -directionToPrevWC;
    }

    vec2 thisSegmentForwardWC, otherSegmentForwardWC;
    if (usePrevious)
    {
        thisSegmentForwardWC = -directionToPrevWC;
        otherSegmentForwardWC = directionToNextWC;
    }
    else
    {
        thisSegmentForwardWC = directionToNextWC;
        otherSegmentForwardWC =  -directionToPrevWC;
    }

    vec2 thisSegmentLeftWC = vec2(-thisSegmentForwardWC.y, thisSegmentForwardWC.x);

    vec2 leftWC = thisSegmentLeftWC;
    float expandWidth = width * 0.5;

    // When lines are split at the anti-meridian, the position may be at the
    // same location as the next or previous position, and we need to handle
    // that to avoid producing NaNs.
    if (!czm_equalsEpsilon(prevEC.xyz - positionEC.xyz, vec3(0.0), czm_epsilon1) && !czm_equalsEpsilon(nextEC.xyz - positionEC.xyz, vec3(0.0), czm_epsilon1))
    {
        vec2 otherSegmentLeftWC = vec2(-otherSegmentForwardWC.y, otherSegmentForwardWC.x);

        vec2 leftSumWC = thisSegmentLeftWC + otherSegmentLeftWC;
        float leftSumLength = length(leftSumWC);
        leftWC = leftSumLength < czm_epsilon6 ? thisSegmentLeftWC : (leftSumWC / leftSumLength);

        // The sine of the angle between the two vectors is given by the formula
        //         |a x b| = |a||b|sin(theta)
        // which is
        //     float sinAngle = length(cross(vec3(leftWC, 0.0), vec3(-thisSegmentForwardWC, 0.0)));
        // Because the z components of both vectors are zero, the x and y coordinate will be zero.
        // Therefore, the sine of the angle is just the z component of the cross product.
        vec2 u = -thisSegmentForwardWC;
        vec2 v = leftWC;
        float sinAngle = abs(u.x * v.y - u.y * v.x);
        expandWidth = clamp(expandWidth / sinAngle, 0.0, width * 2.0);
    }

    vec2 offset = leftWC * expandDirection * expandWidth * czm_pixelRatio;
    return vec4(clippedPositionWC.xy + offset, -clippedPositionWC.z, 1.0) * (czm_projection * clippedPositionEC).w;
}

vec4 getPolylineWindowCoordinates(vec4 position, vec4 previous, vec4 next, float expandDirection, float width, bool usePrevious, out float angle)
{
    vec4 positionEC = czm_modelViewRelativeToEye * position;
    vec4 prevEC = czm_modelViewRelativeToEye * previous;
    vec4 nextEC = czm_modelViewRelativeToEye * next;
    return getPolylineWindowCoordinatesEC(positionEC, prevEC, nextEC, expandDirection, width, usePrevious, angle);
}